Generalized derivations acting on multilinear polynomials in prime rings
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Basudeb Dhara (2018)
Czechoslovak Mathematical Journal
Oukhtite, L., Salhi, S., Taoufiq, L. (2010)
Beiträge zur Algebra und Geometrie
Huang, Shuliang (2007)
International Journal of Mathematics and Mathematical Sciences
Basudeb Dhara, Sukhendu Kar, Sachhidananda Mondal (2015)
Czechoslovak Mathematical Journal
Let be a prime ring with its Utumi ring of quotients and extended centroid . Suppose that is a generalized derivation of and is a noncentral Lie ideal of such that for all , where is a fixed integer. Then one of the following holds:
Feng Wei, Zhankui Xiao (2009)
Rendiconti del Seminario Matematico della Università di Padova
Nurcan Argaç, Vincenzo De Filippis, H. G. Inceboz (2008)
Rendiconti del Seminario Matematico della Università di Padova
Abderrahman Hermas, Abdellah Mamouni, Lahcen Oukhtite (2024)
Mathematica Bohemica
Let be a prime ring and a nonzero ideal of The purpose of this paper is to classify generalized derivations of satisfying some algebraic identities with power values on More precisely, we consider two generalized derivations and of satisfying one of the following identities:
Shuliang Huang (2019)
Communications in Mathematics
Let be a prime ring with center and a nonzero right ideal of . Suppose that admits a generalized reverse derivation such that . In the present paper, we shall prove that if one of the following conditions holds: (i) , (ii) , (iii) , (iv) , (v) , (vi) for all , then is commutative.
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